Mathematics
A rain gutter is formed by bending up the sides of a 44-inch-wide rectangular me

Question Description

(a) Find a function that models the cross-sectional area of the gutter in terms of x.

A(x) = 


(b) Find the value of x that maximizes the cross-sectional area of the gutter.
x =  in


(c) What is the maximum cross-sectional area for the gutter?
 in2

Final Answer

Okie Since i dont know how the bent is done, Its either curvy or in right angled,I am assuming that the bent is done in right angle 

STEP1: EXPRESSION FOR CROSS SECTIONAL AREA 

 x --> The inches by which the sides are bent 

Cross Sectional Area = x (44-2x) or 44x-2x^2

STEP 2; FIND THE VALUE OF X USING PARABOLA EXPRESSION 

Now we have to find x. To find that lets imagine a parabola from which x can be found as 

x=(-b)/2a  ----> in our expression above we have a=-2; b=44

x=(-44)/(2*-2) = 11

STEP 3; SUB THE VALUE OF X to AREA FUNCTION 

Now that we know x we can find the area by substituting the value 

Area = (x)(44-2x) ==>(11)(44-22)==>(11)(22)==> 242 square inches

Cornell University

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